Soliton Phase Research Articles

The propagation of spiraling elliptic sine soliton in nonlocal nonlinear media

Abstract We study a novel spiraling elliptic sine soliton (SESS) in nonlocal nonlinear media by split-step Fourier method, and find that the profile and phase of such soliton have complicated structures. Numerical results show that the topological charge and ellipticity have profound effects on the propagation dynamics of SESS. Concretely, for the same ellipticity, the different topological-charge SESS have the same critical power, cross-term phase coefficient, rotation period, and different critical orbital angular momentums (OAM). However, the critical power, cross-term phase coefficient, rotation period and OAM will increase as the increase of ellipticity. In addition, as the ellipticity and topological charge increase, the stability of the beam will decrease.

On the phase and group velocities of optical solitons

The method of analytical continuation of the dispersion parameters on the complex plane is analyzed. On this basis the new general formulae for phase and group velocities of the soliton-like pulses are obtained.

Ultrafast all-optical ALU operation using a soliton control within the cascaded InGaAsP/InP microring circuits

A dark-bright soliton conversion is used to perform the two arithmetic logic unit operations namely adder and subtractor operations. The advantage of the system such as power stability, non-dispersion and the dark-bright soliton phase conversion control can be obtained. The input source into the circuit is the bright soliton pulse, with the pulse width of 35 ps, the peak power at 1.55 µm is 1 mW. By using the dark-bright soliton conversion pair, the generated logic bits can be controlled, and the secure bits can be achieved. The simulation results show the output signal with a minimum loss of only 0.1% with respect to a low input power of 1 mW, and ultra-fast response time of about 1 ps can be achieved. It gives the ultra-high bandwidth of more than 40 Gbits−1. The circuit composes six microring resonators made of InGaAsP/InP material with smaller ring radii of 1.5 µm, and the total physical scale of the circuit less than 100 µm2.

Theory of magnetoelastic resonance in a monoaxial chiral helimagnet

We study magnetoelastic resonance phenomena in a mono-axial chiral helimagnet belonging to hexagonal crystal class. By computing the spectrum of coupled elastic wave and spin wave, it is demonstrated how hybridization occurs depending on their chirality. Specific features of the magnetoelastic resonance are discussed for the conical phase and the soliton lattice phase stabilized in the mono-axial chiral helimagnet. The former phase exhibits appreciable non-reciprocity of the spectrum, the latter is characterized by a multi-resonance behavior. We propose that the non-reciprocal spin wave around the forced-ferromagnetic state has potential capability to convert the linearly polarized elastic wave to circularly polarized one with the chirality opposite to the spin wave chirality.

Optimal control of dark solitons

We consider optimal control methods for dark solitons and their higher-order states based on the completely integrable nonautonomous nonlinear Schrödinger equation (NLSE) models with varying gravitational-like and harmonic oscillator potentials, and in the presence of gain or absorption. In view of the fact that the time-dependence of the dark soliton phase (chirp) represents a major difference between bright and dark solitons, our main goal here is to gain a deeper understanding at a fundamental level based on the Lax pairs of how this time-dependent phase appears in the framework of the nonautonomous NLSE models with varying dispersion and nonlinearity. Specifically, we consider dynamics of dark solitons and their higher-order states in a variety of different optical scenarios. The main features of dark solitons are supplied by numerical calculations performed both for the exactly integrable and nonintegrable cases. We reveal nontrivial dynamics of black and gray solitons under the optimal control conditions. Since the experimental realization of dark solitons is possible only if a finite background pedestal is used, we consider dynamics of dark solitons and their higher-order states superimposed on the ground state of nonlinear harmonic oscillator. Direct numerical experiments performed in the framework of the Gross-Pitaevskii (GP) model in a broad range of parameters reveal many fundamental features of the dark solitons dynamics in confining harmonic oscillator potential, including the background BEC cloud spreading near the Feshbach resonance (when repulsive nonlinearity has a dispersive form). One of the most important effects is related to the “saturation” of the maximum value of self-compression near the Feshbach resonance. This effect exists both for the central black soliton and for the gray solitons formed during the higher-order dark soliton oscillations in the parabolic trap. The soliton becomes black at the turning points in the harmonic potential and gray at the trap center. This makes possible to observe the nontrivial dynamics of the periodic transformation of the black soliton to the gray one.

Hydrodynamic optical soliton tunneling.

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Soliton-induced critical current oscillations in two-band superconducting bridges

Using time-dependent Ginzburg-Landau theory we find oscillations of critical current density $j_c$ as a function of the length $L$ of the bridge formed from two-band superconductor. We explain this effect by appearance of the phase solitons in the bridge at $j<j_c$, those number changes with change of $L$. In case of sufficiently strong interband coupling oscillations of $j_c$ disappear.

Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser

Dissipative solitons are remarkably localized states of a physical system that arise from the dynamical balance between nonlinearity, dispersion and environmental energy exchange. They are the most universal form of soliton that can exist, and are seen in far-from-equilibrium systems in many fields, including chemistry, biology and physics. There has been particular interest in studying their properties in mode-locked lasers, but experiments have been limited by the inability to track the dynamical soliton evolution in real time. Here, we use simultaneous dispersive Fourier transform and time-lens measurements to completely characterize the spectral and temporal evolution of ultrashort dissipative solitons as their dynamics pass through a transient unstable regime with complex break-up and collisions before stabilization. Further insight is obtained from reconstruction of the soliton amplitude and phase and calculation of the corresponding complex-valued eigenvalue spectrum. These findings show how real-time measurements provide new insights into ultrafast transient dynamics in optics. The simultaneous use of dispersive Fourier transform and time-lens measurements allows complete characterization of the unstable spectral and temporal evolution of ultrashort dissipative solitons, providing further insight into ultrafast transient dynamics in optics.

Experimental formation of a fractional vortex in a superconducting bi-layer

We report the experimental formation of a fractional vortex generated by using a thin superconducting bi-layer in the form of a niobium bi-layer, observed as a magnetic flux distribution image taken by a scanning superconducting quantum interference device (SQUID) microscope. Thus, we demonstrated that multi-component superconductivity can be realized by an s-wave conventional superconductor, because, in these superconductors, the magnetic flux is no longer quantized as it is destroyed by the existence of an inter-component phase soliton (i-soliton).

Флуктуационное образование фазовых солитонов в двузонных сверхпроводящих мостиках

Abstract —Based on the Ginzburg–Landau theory, the dependence of the threshold energy δ F _thr of formation of a phase slip center from the current for a superconducting two-band bridge has been calculated. It has been found that, in the case of sufficiently long bridges and a weak interband Josephson coupling, there is a range of currents at which fluctuation transition from the state of the zero interband phase difference to the states with a phase soliton is possible, which manifests itself in a considerable decrease in the threshold energy δ F _thr, and a fluctuation change in the number of phase solitons in the bridge. In the case of a strong interband coupling, no fluctuation formation of phase solitons occurs and the dependence δ F _thr( I ) tends to the expression obtained earlier by Langer and Ambegaokar for a single-band superconductor.

Stable optical soliton in the ring-cavity fiber system with carbon nanotube as saturable absorber

Main attention focuses on the theoretical study of the ring-cavity fiber laser system with carbon nanotubes (CNT) as saturable absorber (SA). The system is modelled as a non-standard Schrödinger equation with the coefficients blended real and imaginary numbers. New stable exact soliton solution is constructed by the bilinear transformation method for the system. The influences of the key parameters related to CNTs and SA on the optical pulse soliton are discussed in simulation. The soliton amplitude and phase can be tuned by choosing suitable parameters.

Extreme events induced by collisions in a forced semiconductor laser.

We report on the experimental study of an optically driven multimode semiconductor laser with a 1m cavity length. We observed a spatiotemporal regime where real-time measurements reveal very high-intensity peaks in the laser field. Such a regime, which coexists with the locked state and with stable phase solitons, is characterized by the emergence of extreme events that produce heavy tail statistics in the probability density function. We interpret the extreme events as collisions of spatiotemporal structures with opposite chirality. Numerical simulations of the semiconductor laser model, showing very similar dynamical behavior, substantiate our evidences and corroborate the description of interactions such as collisions between phase solitons and transient structures with different phase rotations.

Formation of phase soliton complexes in an optically injected semiconductor laser

We show experimental and numerical results about attractive interactions between phase solitons in a strongly multimode semiconductor laser with injected signal. The formation of soliton bound states, or phase solitons with multiple chiral charge, is demonstrated and analyzed in terms of the (spatio-temporally resolved) phase dynamics of the system. Propagation velocity of phase solitons in the longitudinal cavity is studied, and a correlation is established with phase soliton size and total charge.

Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates

We investigate the dynamics of a spin-orbit (SO) coupled BECs in a time dependent harmonic trap and show the dynamical system to be completely integrable by constructing the Lax pair. We then employ gauge transformation approach to witness the rapid oscillations of the condensates for a relatively smaller value of SO coupling in a time independent harmonic trap compared to their counterparts in a transient trap. Keeping track of the evolution of the condensates in a transient trap during its transition from confining to expulsive trap, we notice that they collapse in the expulsive trap. We further show that one can manipulate the scattering length through Feshbach resonance to stretch the lifetime of the confining trap and revive the condensate. Considering a SO coupled state as the initial state, the numerical simulation indicates that the reinforcement of Rabi coupling on SO coupled BECs generates the striped phase of the bright solitons and does not impact the stability of the condensates despite destroying the integrability of the dynamical system.

Study on soliton phase characteristics in 100 Gbps single‐channel telecommunication system

SummaryHere, we demonstrate the peculiar particle nature of soliton pulses with relative to phase, where the adjacent soliton pulses in a sequence attract and repel each other periodically for in‐phase and out‐of‐phase arrangement, respectively. This effect of soliton's interaction and repulsion is studied analytically by using perturbation theory approach. The study of soliton pair characteristics are mainly noted for different relative spacing (qo) between them and for different phase of launched soliton pulses. Following the analytical studies, we analyzed the effect in a 100 Gbps, single channel and uncompensated telecommunication system for different phased soliton sequences. Such that, the performance of the telecommunication system is characterized in terms of Q‐factor (Q) and bit‐error rate to realize the influence of phase on soliton pulses. The system was studied for 1 collision length (LD) of 123.36 km. It is seen that, for 100 Gbps system implemented with standard single mode telecom fiber, with soliton spaced at qo = 5.28, the in‐phase pulses interacted at 61.68 km, which has resulted in Q = 0 (bit‐error rate = 1). It is realized that for small‐phase introduction on soliton pulses, the system yielded fair Q demonstrating the non‐interaction at the Ip as the pulses deviate with respect to increasing phase values. But, it is also shown that large phase between pulses introduces more deviation, which results in overlapping of deviated pulses with adjacent pulses in sequence resulting in degradation of high bitrate system performance.

Phase Space Analysis and Soliton Solution for Quartic Potential

Phase Space Analysis and Soliton Solution for Quartic Potential

Controllable behaviors of nonautonomous solitons on background of continuous wave and cnoidal wave in $$\mathcal {PT}$$ PT -symmetric dimer with inhomogeneous effect

We obtain exact \(\mathcal {PT}\)-symmetric and \(\mathcal {PT}\)-antisymmetric nonautonomous soliton solutions on background waves. These solutions indicate that dispersion and nonlinear coefficients influence form factors of nonautonomous solitons such as amplitude, width and center; however, linear coupling coefficient and gain/loss parameter only influence phase of solitons. Based on these solutions, the controllable behaviors such as postpone, sustainment and restraint on continuous wave background in an exponential decreasing dispersion system are discussed. Moreover, the propagation behaviors of solitons on the cnoidal wave background in different dispersion systems are also studied.

One-dimensional optical solitons in cubic–quintic–septimal media with $$\varvec{\mathcal {PT}}$$ PT -symmetric potentials

A (\(1+1\))-dimensional inhomogeneous cubic–quintic–septimal nonlinear Schrodinger equation with \(\mathcal {PT}\)-symmetric potentials is studied, and two families of soliton solutions are obtained. From soliton solutions, the amplitude of soliton is independent of the \(\mathcal {PT}\)-symmetric potential parameter k; however, the phase depends on the parameter k. The phase of soliton alters from negative to positive values at the location of center. Moreover, the evolutional behaviors of these solitons are discussed.

Phase Competition, Solitons, and Domain Walls in Neutral–Ionic Transition Systems

Phase competition and excitations in the one-dimensional neutral-ionic transition systems are theoretically studied comprehensively. From the semiclassical treatment of the bosonized Hamiltonian, we examine the competition among the neutral (N), ferroelectric-ionic (I$_\mathrm{ferro}$) and paraelectric-ionic (I$_\mathrm{para}$) states. The phase transitions between them can become first-order when the fluctuation-induced higher-order commensurability potential is considered. In particular, the description of the first-order phase boundary between N and I$_\mathrm{ferro}$ enables us to analyze N-I$_\mathrm{ferro}$ domain walls. Soliton excitations in the three phases are described explicitly and their formation energies are evaluated across the phase boundaries. The characters of the soliton and domain-wall excitations are classified in terms of the topological charge and spin. The relevance to the experimental observations in the molecular neutral-ionic transition systems is discussed. We ascribe the pressure-induced crossover in tetrathiafulvalene-$p$-chloranil (TTF-CA) at a high-temperature region to that from the N to the I$_\mathrm{para}$ state, and discuss its consequence.

Straight line shifts of time-domain trajectories of soliton pulses with initial first-order phase modulation in optical fibers

The nonlinear propagation of hyperbolic secant soliton optical pulses with initial first-order phase modulation in the anomalous dispersion regions of optical fibers are investigated numerically. The corresponding evolutions of pulse shapes and spectra are provided for different soliton order and phase modulation parameters. The results show that, in the time domain, the initially first-order phase modulation can make the soliton pulse shift towards the pulse leading or trailing edges along a straight line with the pulse shape profile and its breather evolution behavior unchanged. Correspondingly, in the frequency domain, the initial first-order phase modulation can make the pulse spectrum exhibit red-shifting or blue-shifting phenomenon with the pulse spectrum profile and its breather evolution behavior unchanged. The larger the absolute value of the phase modulation parameter, the larger the shifting. While for the same phase modulation parameter, both the fundamental- and higher-order solitons exhibit the same shifting. These results may be potentially applied in manipulating the time-domain trajectories of the solitons as well as their corresponding frequency-domain positions by engineering the initial first-order phase modulation parameters of the solitons.